Semiparametric Dynamic Logit Model with Endogenous Networks

This paper develops identification and estimation methods for dynamic partially linear logit models when social networks are endogenous and evolve over time. The outcome equation includes a lagged dependent variable and an unknown function of time-varying unobserved social characteristics that also govern link formation. Standard panel logit approaches, including those augmented with network controls, produce biased estimates when these latent traits are present. I show that combining conditional likelihood arguments with network-type matching across agents eliminates both individual heterogeneity and the unknown social influence function, achieving point identification of the slope parameters and the state dependence coefficient without imposing parametric restrictions on the network formation process. I propose a feasible kernel-weighted conditional maximum likelihood estimator that matches agents using codegree similarity and local smoothing over time-adjacent covariates. Consistency and asymptotic normality are established under weak regularity conditions. Monte Carlo simulations demonstrate that the estimator substantially reduces bias relative to standard dynamic logit specifications across a range of network formation mechanisms and sample sizes. An empirical application to adolescent smoking behavior using longitudinal friendship network data illustrates the method and suggests that standard approaches overestimate state dependence by confounding it with endogenous network sorting.